“The Problem in the “Nerd Sniping” xkcd Comic” by peralice

A few days ago I saw this comic reposted, and I thought: wait! Unlike every prior time I have seen this comic, I actually know how to solve this now! One thing which I often find really cool, and which I don’t think comes up a lot in most people's mathematical education, is when you can learn something about some thing non-random by analysing a random process. So, let me show you a way to find out the resistance between two points in a circuit by instead finding out the number of times someone randomly walking around that circuit will step on those points. Equivalent Resistance Here's a closeup of the problem: You may be familiar with the rules for series and parallel resistors from high school: if there are some resistors in series (one after another), this is “equivalent to” having a single resistor in the circuit which has a resistanceequal to the sum of their resistances. That is, if you replace the resistors with just one of resistance , the behaviour of the rest of the circuit will be the same. Some resistors in series If there are some resistors in parallel, this is “equivalent to” having [...] ---Outline:(00:54) Equivalent Resistance(02:20) Circuit Laws(05:57) A System of Equations(08:44) Random Walks(11:22) The Potential Function(14:14) Fourier Analysis(18:00) Recap The original text contained 5 footnotes which were omitted from this narration. --- First published: April 28th, 2026 Source: https://www.lesswrong.com/posts/xdkZSeSQN4bA8hmrb/the-problem-in-the-nerd-sniping-xkcd-comic --- Narrated by TYPE III AUDIO. ---Images from the article:Apple Podcasts and Spotify do not show images in the episode description. Try Pocket Casts, or another podcast app.